Capillary Coarsening Drives Re-entrant Statistical Transitions in Early Coffee-Ring Growth

Understanding how nonequilibrium systems evolve between distinct statistical regimes remains a fundamental challenge in statistical physics. Here we show that particle deposition at an evaporating contact line provides an experimental realization of cooperative one-dimensional deposition, in which post-deposition capillary attraction drives particles to migrate, cluster, and coarsen. As deposition proceeds, the cluster-width distribution undergoes a striking re-entrant transition, evolving from an initial exponential form to a peaked Gamma distribution and subsequently returning to an exponential form. This dynamic transition is accompanied by a non-monotonic crossover in fluctuation scaling, $σ_w\sim\langle w\rangle^κ$, with $κ$ changing successively from $1$ to $1/2$ and back to $1$. Monte Carlo simulations reproduce these statistical transitions. Our results establish evaporative contact-line deposition as a simple model of correlated one-dimensional assembly and reveal how local interactions can produce re-entrant statistical behaviour in a nonequilibrium system.